Why sacrificing Grandma by opening up again might not save the economy

Great Debates
3

Let’s assume the following:

  1. The average person can generate about $2500 worth of value per month, if employed.
  2. There is a linear scale of social distancing (e.g., cutting off airplanes, cutting off events, shelter-at-home, forced complete quarantine for all, etc.) which causes 5% unemployment if we do nothing (0) and 15% employment at the top end (10).
  3. The fatality rate for people under 55 is 0.15% and 5% for those 55 and older. This is, assuming that hospitals are able to adequately care for them.
  4. If hospitals have become overrun, then the fatality rate is tripled in direct correlation to the percentage of overrun hospitals.
  5. 80% of the labor force is under the age of 55.
  6. The percentage of hospitals which are overrun is linearly correlated to the scale of social distancing. At 0, 50% will be overrun. At 10, 0% will be overrun.
  7. The duration of the epidemic is linearly correlated to the scale of social distancing. At 0, the epidemic will factor on employment rates for a 3 month period. At 10, it will be stretched over a 6 month period.
  8. The percentage of infected is linearly correlated to the scale of social distancing. At 0, 60% of individuals will become infected. At 10, 30% will.
  9. The average age of a worker is 42. The average retirement age of a worker is 62. Any deaths (for simplicity’s sake) will be viewed as a loss of 20 years worth of economic activity.

While these numbers are somewhat ballpark, they are generally based on these cites:

If we perform a social isolation level of 8 across the entire worker population, we expect a fatality rate (among workers) of:

workerCount = 150m
workersInfected = (workerCount * ((1.0 - 0.8) * (0.6 - 0.3) + 0.3)) = 54m
youngWorkerFatalitiesPreHospital = (workersInfected * 0.8) * 0.0015 = 64,800
olderWorkerFatalitiesPreHospital = (workersInfected * 0.2) * 0.05 = 540,000
youngWorkerFatalities = youngWorkerFatalitiesPreHospital * ((1 - 0.8) * 0.5 * 2 + 1) = 77,760
olderWorkerFatalities = olderWorkerFatalitiesPreHospital * ((1 - 0.8) * 0.5 * 2 + 1) = 648,000
totalFatalities = youngWorkerFatalities + olderWorkerFatalities = 725,760

And we expect an economic loss of:

lossesToDeath = totalFatalities * $2500 * 12 * 20 = $435.5b
totalUnemployed = (0.8 * (0.15 - 0.5) + 0.5) * workerCount = 87m
totalMonthsUnemployed = (0.8 * (6 - 3) + 3) = 5.4
totalLossesToUnemployment = totalMonthsUnemployed * totalUnemployed * $2500 = $1.2t
totalLoss = lossesToDeath + totalLossesToUnemployment = $1.6t

Versus a 2:

workerCount = 150m
workersInfected = (workerCount * ((1.0 - 0.2) * (0.6 - 0.3) + 0.3)) = 81m
youngWorkerFatalitiesPreHospital = (workersInfected * 0.8) * 0.0015 = 97,200
olderWorkerFatalitiesPreHospital = (workersInfected * 0.2) * 0.05 = 810,000
youngWorkerFatalities = youngWorkerFatalitiesPreHospital * ((1 - 0.2) * 0.5 * 2 + 1) = 174,960
olderWorkerFatalities = olderWorkerFatalitiesPreHospital * ((1 - 0.2) * 0.5 * 2 + 1) = 1,458,000
totalFatalities = youngWorkerFatalities + olderWorkerFatalities = 1,632,960

lossesToDeath = totalFatalities * $2500 * 12 * 20 = $979.8b
totalUnemployed = (0.2 * (0.15 - 0.5) + 0.5) * workerCount = 78m
totalMonthsUnemployed = (0.2 * (6 - 3) + 3) = 3.6
totalLossesToUnemployment = totalMonthsUnemployed * totalUnemployed * $2500 = $702b
totalLoss = lossesToDeath + totalLossesToUnemployment = $1.7t

Not a particularly rigorous analysis but the biggest difference seems to be life rather than economics.